This is one of the main topics explored by the interesting book Remedy and Reaction by Paul Starr. The U.S. has gotten close to national health insurance programs a number of times. One of the first times was in New York after World War I.
The one state where compulsory health insurance came close to passage was New York…In March 1919…the New York State Senate…[passed] a health-insurance bill that had the support of the recently elected Democratic governor Al Smith…
If New York had adopted a health insurance program in 1919,it might have had national ramifications. The unemploymen tinsurance program that Wisconsin adopted in 1932 helped pave the way for federal legislation in 29135. In Canada, the health insurance plan adopted in Saskatchewan in 1946 played a comparable role as a stepping stone toward a national program.
Private health insurance in the US developed out of the need to finance the high cost of hospital services. In the early 20th century, health insurance was most valuable for replacing wages and providing a funeral benefit. As the cost of medical care care grew in the late 1920s and 1930s, the value of health insurance to cover medical cost grew.
…in the late 1920s and early 1930s individual hospitals and hospital associations in Texas, California and other states created the first plans for groups of employees to buy insurance for hospital expenses. These plans, which evolved into the Blue Cross system, were run on a non-profit basis and at first covered only a small number of people…
Another reason why nationalized health insurance has not passed is that physician have generally been opposed to government health insurance.
In the late nineteenth and early twentieth centuries, legislatures enacted progressively stricter licensing laws for doctors, raising requirements for medical education; the effect of those laws was to close many medical schools and reduce the supply of physicians at a time when demand for their services was growing. Under these conditions, doctors were able to increase their fees and incomes (which was one reason why organized professional support for government health programs diminished).
Many government health insurance programs would pay physicians based on global capitation, which would likely drive down demand and wages, particularly for specialist services.